In a paper recently published in the Proceedings of the National Academy of Sciences, physicist Tim Palmer of the University of Oxford in the United Kingdom has proposed a slight change to the mathematics underlying quantum theory. The framework, called “Rational Quantum Mechanics”, would effectively place an upper limit on quantum hardware capacity.
If valid, this means that the quantum capacity will not increase infinitely. After this, whatever excitement or fear we generate from their abilities subsides. For example, they would not be as much of a threat to RSA cryptosystems, the protective algorithms used to store most data today, despite countless claims that quantum computers could crack them.
ambitious intentions
But that’s all a big “if.” For one, quantum mechanics is one of the most successful theories in the history of science. Of course, there is still a lot about the quantum world that we don’t understand, but it’s an ambitious step to suggest that some changes to the theory are needed.
Palmer agrees but still believes that some mathematical aspects can be modified to better represent reality. Furthermore, their idea may be testable with existing quantum technologies within the next five years.
In particular, Palmer focuses on a concept called Hilbert space – the standard vector space that is used to compute most quantum systems. Compared to classical physics, quantum mechanics is “more dependent on the continuity of the real numbers…”[but] Nature abhors continuity,” Palmer said in a statement.
here is the plan
In classical quantum mechanics, the number of dimensions in a Hilbert space grows exponentially with the number of qubits. According to a column in Quantum Insider, this is “crucial to delivering on the promise of exponential scaling quantum computing, which enables algorithms like Shor’s method to factor large numbers far faster than classical machines.”
Palmer’s suggestion is as follows: For practical purposes, physical space resembles a collection of discrete elements, not a continuous one. “Rational” quantum mechanics subscribes to this view of geometric space, and as a result the information content in a quantum state grows linearly with the number of qubits.
“Above a critical number of entangled qubits, there is not enough information in the quantum state to assign even one bit of information to each dimension of the Hilbert space,” Palmer explained. “When this happens, quantum algorithms using the entire Hilbert space will stop having a quantum advantage over classical algorithms.”
According to the paper, quantum computers will lose their advantage when the system exceeds about 1,000 qubits. A big selling point of quantum computers is that they will be able to factor very large numbers in a way that classical computers cannot. That infinite factoring capability is relevant to claims that quantum computers can crack the RSA algorithm. Therefore, there is a limit to how many qubits engineers can stuff into the most “powerful” quantum computer – after 1,000 qubits, the system will tap out long before it reaches the required scale. In case you’re wondering, this limit is much lower than the common estimate of the number of qubits needed to break RSA: 4,099.
burden of proof
Although an attractive proposal, rational quantum mechanics remains highly speculative. Only time and testing will tell how much this proposal might change things for better or for worse. In the paper, Palmer proposes an experimental test to entangle multiple qubits according to a specific algorithm and check for any signs of poor performance.
Again, quantum mechanics is one of the most empirically tested theories. Palmer is correct that Hilbert space is more of an “idealization”, as he says in the statement, but no experiments have been done to indicate the type of discrete physical space described by Palmer in his proposal.
Personally, I don’t want to discredit the new idea too much. It’s foolish to assume that something is “impossible” when quantum things are involved. But big claims require big evidence, and if this theory turns out to be anything like that, I’ll be first in line to learn more.
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